Hemisphere Calculator

How it is calculated

The only input is the radius r, which must be greater than zero. Volume is half that of a sphere: V = (2/3) × π × r³. The surface figure is the total surface area: S = 3 × π × r², which is the curved dome 2πr² plus the flat circular base πr². Both are rounded to two decimals. Use any length unit; volume comes out in its cube and the surface in its square. Because the surface value includes the base, it is the right figure for a closed solid, but for an open bowl or a dome sitting on the ground you would use only the curved part, which is two thirds of the displayed value.

Common mistakes

• Entering the diameter as the radius. The radius is half the diameter, and since volume goes with the cube, this error makes the volume 8 times too big.
• Using the surface result for an open dome or bowl. It includes the flat base; remove πr² if there is no lid.
• Mixing units, for example a radius in centimeters but expecting liters. The volume is in cubic centimeters; 1,000 cm³ is 1 liter.
• Applying it to a dome that is less than half a sphere, such as a shallow cap. The formulas are only for an exact half.
• Forgetting that doubling the radius multiplies volume by 8 and surface by 4.